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Topics: Radio Program, National security, Political terminology, Continents, Radio formats, Political...

Topics: san francisco, algebra, wynns

Source: Comcast Cable

Topics: Radio Program, Elections, G20 nations, Stock market, Climate change, Economic problems, NPR...

Topics: Radio Program, Firearm actions, Firearms, Gun politics, Weapons, Sources of law, Cricket...

Topics: Radio Program, G20 nations, Stock market, Elections, Holidays, Human geography, Republics, Member...

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Topics: Radio Program, American Roman Catholics, Archaeological artefact types, Guggenheim Fellows,...

Topics: Radio Program, Public services, Social security, Insurance, Financial markets, Personal finance,...

Topics: Radio Program, Space stations, Artificial satellites orbiting Earth, Human spaceflight, Sleep,...

Topics: Radio Program, Prosecution, Health, American mob bosses, Types of university or college, Legal...

Topics: Radio Program, Patent law, Spirituality, Engineering, Pseudoscience, New Thought beliefs, American...

Topics: Radio Program, Patent law, Spirituality, Engineering, Pseudoscience, New Thought beliefs,...

Topics: Radio Program, Geriatrics, Health care, Nursing, Health, Multinational companies, Healthcare...

Topics: Radio Program, American talk radio hosts, American political pundits, Jewish American writers,...

Topics: Radio Program, Training, Taxation, Mortgage, Government, American magazines, Macroeconomics,...

Topics: Radio Program, Yale University alumni, Intelligent design advocates, American Orthodox Jews, Email,...

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Topics: Radio Program, National security, Mountain ranges of Colorado, Christmas, Commerce, Special forces,...

Topics: Radio Program, American politicians, American Roman Catholics, Harvard Law School alumni, American...

Topics: Radio Program, Learning disabilities, Dementia, Alzheimer's disease, Neurological disorders,...

Topics: Radio Program, American male singers, Country code top-level domains, Rooms, Food and drink, Algebra

Topics: Radio Program, Business law, Regions of California, Credit cards, Fair trade organizations,...

Topics: Radio Program, Chief executive officers, States of the Confederate States of America,...

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Topics: Radio Program, Mystics, School types, Christian terms, Subjects taught in medical school,...

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3.0

Jun 30, 2018
06/18

by
Sara Oriana Gomes Tavares

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We propose a new type of state sum model for two-dimensional surfaces that takes into account topology and spin. The definition used - new to the literature - provides a rich class of extended models called spin models. Both examples and general properties are studied. Most prominently, we find this type of model can depend on a surface spin structure through parity alone and we explore explicit cases that feature this behaviour. Further directions for the two dimensional world are analysed: we...

Topics: Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1412.5506

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2.0

Jun 30, 2018
06/18

by
Alexander Schrijver

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We give necessary and sufficient conditions for a weight system on multiloop chord diagrams to be obtainable from a metrized Lie algebra representation, in terms of a bound on the ranks of associated connection matrices. Here a multiloop chord diagram is a graph with directed and undirected edges so that at each vertex precisely one directed edge is entering and precisely one directed edge is leaving, and each vertex is incident with precisely one undirected edge. Weight systems on multiloop...

Topics: Quantum Algebra, Mathematics, Combinatorics, Representation Theory

Source: http://arxiv.org/abs/1412.6932

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Jun 30, 2018
06/18

by
Teodor Banica

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We study the 10 noncommutative spheres obtained by liberating, twisting, and liberating+twisting the real and complex spheres $S^{N-1}_\mathbb R,S^{N-1}_\mathbb C$. At the axiomatic level, we show that, under very strong axioms, these 10 spheres are the only ones. Our main results concern the computation of the quantum isometry groups of these 10 spheres, taken in an affine real/complex sense. We formulate as well a proposal for an extended formalism, comprising 18 spheres.

Topics: Mathematics, Quantum Algebra, Operator Algebras

Source: http://arxiv.org/abs/1412.7478

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Jun 30, 2018
06/18

by
Keiichi Shigechi

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We construct Laurent polynomial solutions of the boundary quantum Knizhnik--Zamolodchikov equation for $U_{q}(\widehat{\mathfrak{sl}}_{2})$ on the parabolic Kazhdan--Lusztig bases. They are characterized by non-symmetric Koornwinder polynomials with the specialized parameters. As a special case, we obtain the solution of the minimal degree.

Topics: Mathematics, Quantum Algebra, Mathematical Physics

Source: http://arxiv.org/abs/1412.7797

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Jun 29, 2018
06/18

by
Yairon Cid Ruiz

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For an arbitrary rational surface parametrization $P(s,t)=(a(s,t),b(s,t),c(s,t),d(s,t)) \in \mathbb{F}[s,t]^4$ over an infinite field $\mathbb{F}$, we show the existence of a $\mu$-basis with polynomials bounded in degree by $O({\max(deg(a),deg(b),deg(c),deg(d))}^{33})$. Our proof depends on obtaining a homogeneous ideal in $\mathbb{F}[s,t,u]$ by homogenizing $a,b,c,d$. Making additional assumptions on this homogeneous ideal we can obtain lower bounds: - If the projective dimension of this...

Topics: Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1611.07506

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2.0

Jun 30, 2018
06/18

by
Naihuan Jing; Jian Zhang

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The multiparameter quantum Pfaffian of the $(p, \lambda)$-quantum group is introduced and studied together with the quantum determinant, and an identity relating the two invariants is given. Generalization to the multiparameter hyper-Pfaffian and relationship with the quantum minors are also considered.

Topics: Quantum Algebra, Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1701.07458

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Jun 30, 2018
06/18

by
Peyman Nasehpour

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In this paper, we generalize McCoy's theorem for the zero-divisors of polynomials and investigate zero-divisors of semimodules and prove that under suitable conditions, the monoid semimodule $M[G]$ has very few zero-divisors if and only if the semimodule $M$ does so. Then we introduce Ohm-Rush and McCoy semialgebras and prove some interesting results for prime ideals of monoid semirings. In the last section of the paper, we investigate the set of zero-divisors of McCoy semialgebras.

Topics: Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1702.00810

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Jun 30, 2018
06/18

by
Shamit Kachru; Arnav Tripathy

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We propose that Borcherds' Fake Monster Lie algebra is a broken symmetry of heterotic string theory compactified on $T^7 \times T^2$. As evidence, we study the fully flavored counting function for BPS instantons contributing to a certain loop amplitude. The result is controlled by $\Phi_{12}$, an automorphic form for $O(2, 26, \mathbb{Z})$. The degeneracies it encodes in its Fourier coefficients are graded dimensions of a second-quantized Fock space for this large symmetry algebra. This...

Topics: High Energy Physics - Theory, Quantum Algebra, Representation Theory, Mathematics

Source: http://arxiv.org/abs/1702.02572

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Jun 30, 2018
06/18

by
Lukas Katthän

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Let $S = k[x_1, \dotsc, x_n]$ be a polynomial ring over a field $k$ and let $M$ be a graded $S$-module with minimal free resolution $\mathbb{F}_\bullet$. Its linear part $lin(\mathbb{F}_\bullet)$ is obtained by deleting all non-linear entries from the differential of $\mathbb{F}_\bullet$. Our first result is an elementary description of $lin(\mathbb{F}_\bullet)$ in the case that $M$ is the Stanley-Reisner ring of a simplicial complex $\Delta$. Indeed, the differential of...

Topics: Combinatorics, Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1702.07765

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Jun 30, 2018
06/18

by
F. Heydari

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Let $R$ be a commutative ring and $M$ be an $R$-module, and let $I(R)^*$ be the set of all non-trivial ideals of $R$. The $M$-intersection graph of ideals of $R$, denoted by $G_M(R)$, is a graph with the vertex set $I(R)^*$, and two distinct vertices $I$ and $J$ are adjacent if and only if $IM\cap JM\neq 0$. For every multiplication $R$-module $M$, the diameter and the girth of $G_M(R)$ are determined. Among other results, we prove that if $M$ is a faithful $R$-module and the clique number of...

Topics: Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1702.08525

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Jun 30, 2018
06/18

by
David Hernandez

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R-matrices are the solutions of the Yang-Baxter equation. At the origin of the quantum group theory, they may be interpreted as intertwining operators. Recent advances have been made independently in different directions. Maulik-Okounkov have given a geometric approach to R-matrices with new tools in symplectic geometry, the stable envelopes. Kang-Kashiwara-Kim-Oh proved a conjecture on the categorification of cluster algebras by using R-matrices in a crucial way. Eventually, a better...

Topics: Mathematical Physics, Representation Theory, Quantum Algebra, Rings and Algebras, Algebraic...

Source: http://arxiv.org/abs/1704.06039

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Jun 30, 2018
06/18

by
Alessandro De Stefani; Craig Huneke; Luis Núñez-Betancourt

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Let $(R,\mathfrak{m},K)$ be a local ring, and let $M$ be an $R$-module of finite length. We study asymptotic invariants, $\beta^F_i(M,R),$ defined by twisting with Frobenius the free resolution of $M$. This family of invariants includes the Hilbert-Kunz multiplicity ($e_{HK}(\mathfrak{m},R)=\beta^F_0(K,R)$). We discuss several properties of these numbers that resemble the behavior of the Hilbert-Kunz multiplicity. Furthermore, we study when the vanishing of $\beta^F_i(M,R)$ implies that $M$ has...

Topics: Mathematics, Commutative Algebra

Source: http://arxiv.org/abs/1412.4266

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Jun 30, 2018
06/18

by
Alborz Azarang

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Fields with only finitely many maximal subrings are completely determined. We show that such fields are certain absolutely algebraic fields and give some characterization of them. In particular, we show that the following conditions are equivalent for a field $E$: 1. $E$ has only finitely many maximal subrings. 2. $E$ has a subfield $F$ which has no maximal subrings and $[E:F]$ is finite. 3. Every descending chain $\cdots\subset R_2\subset R_1\subset R_0=E$ where each $R_i$ is a maximal subring...

Topics: Mathematics, Commutative Algebra

Source: http://arxiv.org/abs/1412.4983

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Jun 28, 2018
06/18

by
Satya Mandal

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Suppose $A=k[X_1, X_2, \ldots, X_n]$ is a polynomial ring over a field $k$ and $I$ is an ideal in $A$. Then M. P. Murthy conjectured that $\mu(I)=\mu(I/I^2)$, where $\mu$ denotes the minimal number of generators. Recently, Fasel \cite{F} settled this conjecture, affirmatively, when $k$ is an infinite perfect field, with $1/2\in k$ {\rm (always)}. We are able to do the same, when $k$ is an infinite field. In fact, we prove similar results for ideals $I$ in a polynomial ring $A=R[X]$, that...

Topics: Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1509.08534

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3.0

Jun 28, 2018
06/18

by
Alain Bruguières

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We introduce Hopf polyads in order to unify Hopf monads and group actions on monoidal categories. A polyad is a lax functor from a small category (its source) to the bicategory of categories, and a Hopf polyad is a comonoidal polyad whose fusion operators are invertible. The main result states that the lift of a Hopf polyad is a strong (co)monoidal action-type polyad (or strong monoidal pseudofunctor). The lift of a polyad is a new polyad having simpler structure but the same category of...

Topics: Category Theory, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1511.04639

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Jun 28, 2018
06/18

by
Lukas Katthän

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We present a monomial ideal $\mathfrak{a} \subset S$ such that $S/\mathfrak{a}$ is not Golod, even though the product on its Koszul homology is trivial. This constitutes a counterexample to a well-known result by Berglund and J\"ollenbeck (the error can be traced to a mistake in an earlier article by J\"ollenbeck). On the positive side, we show that if $R$ is a monomial ring such that the $r$-ary Massey product vanish for all $r \leq \max(2, \mathrm{reg} R-2)$, then $R$ is Golod. In...

Topics: Commutative Algebra, Combinatorics, Algebraic Topology, Mathematics

Source: http://arxiv.org/abs/1511.04883

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3.0

Jun 28, 2018
06/18

by
Idan Eisner

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Using the notion of compatibility between Poisson brackets and cluster structures in the coordinate rings of simple Lie groups, Gekhtman Shapiro and Vainshtein conjectured a correspondence between the two. Poisson Lie groups are classified by the Belavin--Drinfeld classification of solutions to the classical Yang Baxter equation. For any non trivial Belavin--Drinfeld data of minimal size for $SL_{n}$, the companion paper constructed a cluster structure with a locally regular initial seed, which...

Topics: Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1511.08234

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Jun 28, 2018
06/18

by
Thomas Creutzig; Shashank Kanade; Andrew R. Linshaw

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Let V be a simple VOA and consider a representation category of V that is a vertex tensor category in the sense of Huang-Lepowsky. In particular, this category is a braided tensor category. Let J be an object in this category that is a simple current of order two of either integer or half-integer conformal dimension. We prove that $V\oplus J$ is either a VOA or a super VOA. If the representation category of V is in addition ribbon, then the categorical dimension of J decides this parity...

Topics: Representation Theory, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1511.08754

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Jun 28, 2018
06/18

by
Louis-Hadrien Robert

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We define a new way to evaluate MOY graphs. We prove that this new evaluation coincides with the classical evaluation by checking some skein relations. As a consequence, we prove a formula which relates the $\mathfrak{sl}_N$ and $\mathfrak{sl}_{N-1}$-evaluations of MOY graphs.

Topics: Representation Theory, Combinatorics, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1512.02370

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3.0

Jun 28, 2018
06/18

by
Alexandru Chirvasitu; Paweł Kasprzak

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The notion of Hopf center and Hopf cocenter of a Hopf algebra is investigated by the extension theory of Hopf algebras. We prove that each of them yields an exact sequence of Hopf algebras. Moreover the exact sequences are shown to satisfy the faithful (co)flatness condition. Hopf center and cocenter are computed for $\mathsf{U}_q(\mathfrak{g})$ and the Hopf algebra $\textrm{Pol}(\mathbb{G}_q)$, where $\mathbb{G}_q$ is the Drinfeld-Jimbo quantization of a compact semisimple simply connected Lie...

Topics: Category Theory, Rings and Algebras, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1512.03749

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3.0

Jun 28, 2018
06/18

by
Anton Khoroshkin; Sergei Merkulov; Thomas Willwacher

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Motivated by the universal obstruction to the deformation quantization of Poisson structures in infinite dimensions we introduce the notion of quantizable odd Lie bialgebra. The main result of the paper is a construction of a highly non-trivial minimal resolution of the properad governing such Lie bialgebras, and its link with the theory of so called quantizable Poisson structures.

Topics: Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1512.04710

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Jun 28, 2018
06/18

by
Mohamad Maassarani

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We study orbit configuration spaces $\mathrm{Cf}_G(n,\mathbb{P}^1_*)$ obtained from the action of a finite homography group $G$ on $\mathbb{P}^1$. We construct a flat connection on the orbit space with values in a Lie algebra $\hat{\mathfrak{p}}_n(G) $. We establish an isomorphism of filtered Lie algebras between $\hat{\mathfrak{p}}_n(G)$, the Malcev Lie algebra of the fundamental group of $\mathrm{Cf}_G(n,\mathbb{P}^1_*)$ and the degree completion of the associated graded to the latter Lie...

Topics: Algebraic Topology, Mathematics, Quantum Algebra

Source: http://arxiv.org/abs/1510.00617

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3.0

Jun 28, 2018
06/18

by
Jaroslaw Wlodarczyk

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Building upon ideas of Hironaka, Bierstone-Milman, Malgrange and others we generalize the inverse and implicit function theorem (in differential, analytic and algebraic setting) to sets of functions of larger multiplicities (or ideals). This allows one to describe singularities given by a finite set of generators or by ideals in a simpler form. In the special Cohen-Macaulay case we obtain a singular analog of the inverse function theorem. The singular implicit function theorem is closely...

Topics: Commutative Algebra, Differential Geometry, Complex Variables, Algebraic Geometry, Mathematics

Source: http://arxiv.org/abs/1510.03480

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2.0

Jun 28, 2018
06/18

by
Jan E. Grabowski; Sira Gratz

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We provide a graded and quantum version of the category of rooted cluster algebras introduced by Assem, Dupont and Schiffler and show that every graded quantum cluster algebra of infinite rank can be written as a colimit of graded quantum cluster algebras of finite rank. As an application, for each k we construct a graded quantum infinite Grassmannian admitting a cluster algebra structure, extending an earlier construction of the authors for k=2.

Topics: Representation Theory, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1510.04109

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3.0

Jun 28, 2018
06/18

by
Sergei Alexandrov; Boris Pioline

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Motivated by mathematical structures which arise in string vacua and gauge theories with N=2 supersymmetry, we study the properties of certain generalized theta series which appear as Fourier coefficients of functions on a twisted torus. In Calabi-Yau string vacua, such theta series encode instanton corrections from $k$ Neveu-Schwarz five-branes. The theta series are determined by vector-valued wave-functions, and in this work we obtain the transformation of these wave-functions induced by...

Topics: Mathematics, Quantum Algebra, Mathematical Physics, High Energy Physics - Theory

Source: http://arxiv.org/abs/1511.02892

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Jun 28, 2018
06/18

by
Frank Himstedt; Peter Symonds

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We prove a recursive formula for the exterior and symmetric powers of modules for a cyclic 2-group. This makes computation straightforward. Previously, a complete description was only known for cyclic groups of prime order.

Topics: Commutative Algebra, Representation Theory, Mathematics

Source: http://arxiv.org/abs/1510.02370

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3.0

Jun 28, 2018
06/18

by
Reza Jafarpoure Golzari; Rashid Zaare-Nahandi

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Unmixed bipartite graphs have been characterized by Ravadra and Villarreal independently. Our aim in this paper is to characterize unmixed r-partite graphs under a certain condition, witch is a generalization of villarreal's theorem on bipartite graphs. Also we give some examples and counterexamples in relevance this subject.

Topics: Commutative Algebra, Combinatorics, Mathematics

Source: http://arxiv.org/abs/1511.00228

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Jun 28, 2018
06/18

by
Nicoletta Cantarini; Victor G. Kac

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We introduce the notion of universal odd generalized Poisson superalgebra associated to an associative algebra A, by generalizing a construction made in [5]. By making use of this notion we give a complete classification of simple linearly compact (generalized) n-Nambu-Poisson algebras over an algebraically closed field of characteristic zero.

Topics: Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1511.04957